What are the benefits to using procedural textures VS image textures?
Theoretically, a procedural texture is better, in the same way a vector graphic is better then a raster image. It has infinite resolution, can cover any surface, doesn't require UV mapping, and can be created without getting of your chair or browsing on the web. 

However, an image texture has advantages to. Sometimes a scene, using image textures, can be finished in under an hour, vs a procedural workflow might take days. Image textures also, if sourced from a photograph, can have natural and realistic qualities a procedural textures might not (unless the procedural texture is really really really good).

In list form:

Procedural Textures Pros:


Infinite resolution
Increased editability
Can be applied to nearly any model without repetition or resolution issues.


Image Textures Pros:


Fast to create download.
Good results easily